Formula:7308

Digital Library of Mathematical Functions ID 19.28.E4

${\displaystyle{\displaystyle\int_{0}^{1}t^{\sigma-1}(1-t)^{c-1}R_{-a}\left(b_{1},b_{2};t,1\right)\mathrm{d}t=\frac{\Gamma\left(c\right)\Gamma\left(\sigma\right)\Gamma\left(\sigma+b_{2}-a\right)}{\Gamma\left(\sigma+c-a\right)\Gamma\left(\sigma+b_{2}\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re\sigma>\max(0,a-b_{2})}}$
${\displaystyle{\displaystyle c=b_{1}+b_{2}>0}}$
${\displaystyle{\displaystyle\Re\sigma>\max(0,a-b_{2})}}$

Symbols List

• ${\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}};\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}$: multivariate hypergeometric function
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle\sigma}}$: parameter
 

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